Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Consider the function.

[tex]\[ f(x) = 2x - 6 \][/tex]

Match each transformation of [tex]\( f(x) \)[/tex] with its description.

[tex]\[ g(x) = 2x - 2 \][/tex]
[tex]\[ \begin{array}{l}
g(x) = 8x - 6 \\
g(x) = 8x - 24 \\
g(x) = 8x - 4 \\
g(x) = 2x - 14 \\
g(x) = 2x - 10 \\
\end{array} \][/tex]

[tex]\[
\begin{array}{l}
\text{compresses } f(x) \text{ by a factor of } \frac{1}{4} \text{ toward the } y\text{-axis} \quad \square \\
\text{stretches } f(x) \text{ by a factor of 4 away from the } x\text{-axis} \quad \square \\
\text{shifts } f(x) \text{ 4 units right} \quad \square \\
\text{shifts } f(x) \text{ 4 units down} \quad \square \\
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Alright, let's take each transformation of [tex]\( f(x) = 2x - 6 \)[/tex] one by one and match it with the descriptions provided:

1. Compresses [tex]\( f(x) \)[/tex] by a factor of [tex]\( \frac{1}{4} \)[/tex] toward the [tex]\( y \)[/tex]-axis:

Compressing [tex]\( f(x) = 2x - 6 \)[/tex] by a factor of [tex]\( \frac{1}{4} \)[/tex] toward the [tex]\( y \)[/tex]-axis means we multiply the coefficient of [tex]\( x \)[/tex] by 4.

[tex]\[ f\left(\frac{x}{4}\right) = 2\left(\frac{x}{4}\right) - 6 = \frac{1}{2}x - 6 \quad (\text{This transformation is not obtained directly from the provided functions, hence discard it}) \][/tex]

Alternatively, compress the entire function:

[tex]\( g(x) = \frac{f(x)}{4} = \frac{2x-6}{4} = \frac{1}{2}x - 1.5 (\text{none match, another discard}) \)[/tex]

The correct function provided for this case would be:

[tex]\( g(x) = 8x - 24 \)[/tex]

2. Stretches [tex]\( f(x) \)[/tex] by a factor of 4 away from the [tex]\( x \)[/tex]-axis:

Stretching [tex]\( f(x) = 2x - 6 \)[/tex] by a factor of 4 means we multiply the entire function by 4:

[tex]\[ g(x) = 4(2x - 6) = 8x - 24 \][/tex]

The function [tex]\( g(x) = 8x - 24 \)[/tex] matches this transformation.

3. Shifts [tex]\( f(x) \)[/tex] 4 units to the right:

Shifting the function to the right by 4 units means we replace [tex]\( x \)[/tex] by [tex]\( x - 4 \)[/tex]:

[tex]\[ f(x - 4) = 2(x - 4) - 6 = 2x - 8 - 6 = 2x - 14 \][/tex]

The function [tex]\( g(x) = 2x - 14 \)[/tex] matches this transformation.

4. Shifts [tex]\( f(x) \)[/tex] 4 units down:

Shifting the function downward by 4 units means we subtract 4 from the whole function:

[tex]\[ f(x) - 4 = (2x - 6) - 4 = 2x - 10 \][/tex]

The function [tex]\( g(x) = 2x - 10 \)[/tex] matches this transformation.

By matching the transformations and descriptions:
- Compresses [tex]\( f(x) \)[/tex] by a factor of [tex]\( \frac{1}{4} \)[/tex] toward the [tex]\( y \)[/tex]-axis: [tex]\( \(g(x) = 8x-24\)[/tex]
- Stretches [tex]\( f(x) \)[/tex] by a factor of 4 away from the [tex]\( x \)[/tex]-axis: [tex]\( \(g(x) = 8x-24\)[/tex]
- Shifts [tex]\( f(x) 4 \)[/tex] units right: [tex]\( \(g(x) = 2x-14\)[/tex]
- Shifts [tex]\( f(x) 4 \)[/tex] units down: [tex]\( \(g(x) = 2x-10\)[/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.